Previously my collaborators and I have analyzed GWAS SNP markers with respect to the genetic contribution to obesity and type II diabetes traits. We used a mixed-effects linear model of all the SNPs to estimate the heritability of a set of traits. In addition, we also estimated the genetic contribution that is shared between traits. We showed that approximately half of the known heritability estimated using classical methods are captured collectively by the common SNPs. Previously, only a small fraction of the heritability could be explained from sets of single SNPs, which led to what has been called the problem of missing heritability. Our work showed that the heritability is not missing but merely hidden in the noise. We also showed that the heritability estimated by the SNPs increases with the number of SNPs, which also indicates that the genetic information may be spread over large segments of the genome. We are continuing the work by validating in other data sets and to look for more specific large scale patterns of in the markers for each phenotype in these data sets as was specified in our original request. We showed that the mixed-effects loses validity when the GWAS markers have too much linkage disequilibrium. We applied the statistical theory of compressed sensing to analyzing GWAS data. This is a method that can find sparse nonzero regression coefficients in data sets where the number of parameters far exceeds the number of samples, which is not possible using classical linear regression methods. More importantly, there is a sharp transition from poor to good recovery as the sample size is increased. We use this transition in an algorithm to extract trait associated loci with high confidence. We can also estimate a lower bound on the number of loci associated with a given trait. I have also participated in a collaborative project to update the software tool Plink. I continue to develop new mathematical and computational tools for genetic analysis.